Will a judge agree with us if my husband and I both agree that a past significant other cannot be around our child?

Generally, if both parties are in agreement and the third party has no legal connection nor rights with respect to the child, then putting appropriate language in your agreement would generally be enforceable by the court pursuant to contract law. Consult with an attorney to discuss the specifics of your situation and your options.

There is no Yes/No answer. In most cases the Judge will try to accommodate the agreement of the parties but this is really at the Judge's discretion.

Whatever you have agreed to must be legal to begin with, a judge cannot agree with something that is illegal. Generally, the judge will agree and enter an order, but whatever was agreed to must be enforceable, and cannot be illegal.